Problem #281

Awesome algorithm
Public 11/28/15 7xp Math 62.5%


Given a vector $ A $ of rational numbers, we define the following transformation :
$ B = \{ 1\times (A_1-A_2), 2\times (A_2-A_3), 3\times (A_3-A_4), \dots \}$

We repeat the process:
$ C = \{ 1\times (B_1-B_2), 2\times (B_2-B_3), 3\times (B_3-B_4), \dots \}$

And so on ...

Consider now the vector
$ Z = \{ B_1, C_1, D_1, \dots \} $

If $ A = \{ \frac{1}{1}, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \dots \} \textrm{ find the first index such as the denominator of } Z_i \textrm{ is } \gt 10^{50} $
Answer format: index,denominator
[My timing: < 1 sec]



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